This book offers supporting material for the comprehensive textbook Mathematical Physics—A Modern Introduction to Its Foundations authored by Sadri Hassani. The book covers mathematical preliminaries and all of Part I in Hassani’s textbook. The subjects covered here include the key topics necessary for physicists to form a solid mathematical foundation: vectors and linear maps, algebras, operators, matrices, and spectral decomposition. In particular, the vector space concept is a central unifying theme in later chapters of Hassani’s textbook. Detailed solutions are provided to one third of the end-of-chapter exercises in the first six chapters of his text. The present volume helps upper-undergraduate and early postgraduate physics students deepen their understanding of the mathematics that they encounter in physics, learn physics more efficiently, and use mathematics with more confidence and creativity. The content is thus presented rigorously but remains accessible to physics students. New exercises are also proposed, some with solutions, some without, so that the total number of unsolved exercises remains unchanged. They are chosen to help explain difficult concepts, amplify key points in Hassani's textbook, or make further connections with applications in physics. Taken together with Hassani's work, the two form a self-contained set and the solutions make detailed reference to Hassani's text. The solutions also refer to other mathematics and physics textbooks, providing entry points to further literature that finds a useful place in the physicist's personal library.

The Harbinger's warnings to America expose an important, untold story, the astounding truth about prophecy hidden from the Christian world. This work is like a sequel, unveiling the mysteries of prophecy. The keys to the enigma that is Bible prophecy consist in knowing these rarely understood truths: America is identified in the Bible and is a major player in prophecy. The books of Job and Isaiah are the foundations of all Bible prophecy. Aliens and giants are also mentioned in God's Word and will play a major role in end-time events.

Quote from the book: "This is more than a book that warns the world of what is about to happen. It is also a book that offers a sure hope for the future. While the winter solstice of 2012 will indeed begin the time of the greatest spiritual darkness the world has ever known, it's not the end. It's not the end of the world; it's not even the end of this age."

This comprehensive student manual has been designed to accompany the leading textbook by Bernard Schutz, A First Course in General Relativity, and uses detailed solutions, cross-referenced to several introductory and more advanced textbooks, to enable self-learners, undergraduates and postgraduates to master general relativity through problem solving. The perfect accompaniment to Schutz's textbook, this manual guides the reader step-by-step through over 200 exercises, with clear easy-to-follow derivations. It provides detailed solutions to almost half of Schutz's exercises, and includes 125 brand new supplementary problems that address the subtle points of each chapter. It includes a comprehensive index and collects useful mathematical results, such as transformation matrices and Christoffel symbols for commonly studied spacetimes, in an appendix. Supported by an online table categorising exercises, a Maple worksheet and an instructors' manual, this text provides an invaluable resource for all students and instructors using Schutz's textbook.